Conformal Sigma Models with Anomalous Dimensions and Ricci Solitons

TL;DR

This paper constructs new Ricci soliton metrics with anomalous dimensions for superconformal sigma models, expanding the class of known solutions and connecting to Ricci-flat metrics in specific limits.

Contribution

It introduces explicit non-Ricci-flat Kahler metrics with anomalous dimensions as target spaces for superconformal sigma models, demonstrating their relation to Ricci-flat metrics.

Findings

Derived new Ricci soliton solutions with U(N) and O(N) symmetries.

Showed these metrics reduce to Ricci-flat Kahler metrics when the anomalous dimension vanishes.

Connected the solutions to canonical line bundles over coset spaces.

Abstract

We present new non-Ricci-flat Kahler metrics with U(N) and O(N) isometries as target manifolds of superconformally invariant sigma models with an anomalous dimension. They are so-called Ricci solitons, special solutions to a Ricci-flow equation. These metrics explicitly contain the anomalous dimension and reduce to Ricci-flat Kahler metrics on the canonical line bundles over certain coset spaces in the limit of vanishing anomalous dimension.